Can we use the shape of an object that is instanced to particles with dynamic paint
Dynamic Paint isn't necessary for this to be done. 

Gleb Alexandrov recently posted a video showing how to use a cloth simulation to achieve damage on an object which matches the shape of the object that is colliding with it as shown here in his video Blender Tutorial: 9 Ways to Destroy Things  https://www.youtube.com/watch?v=wJFE2pb0Ri4 

Fist step: add a cloth simulation to the object that you want to have a worn-down damaged look.  To have the object become squashed without bouncing around or flattening out, just set 'Bending' to 0.0   



Then you add a collision simulation to the object that will be causing the damage.  I used default settings for this.



Now use the Timeline to animate the damage-causing object to overlap with the cloth simulation object that is to receive the damage.